Properties of Exponents

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Properties of Exponents

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Properties of Exponents

From the basic definition of positive integer exponents, we have

(1)
$a^{n_1} a^{n_2} = a^{n_1 + n_2}$
(2)
$\
Note that property (2) implies property (1). We list it explicitly for convenience below.

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